Section 8: Potential Long-Term Applications: Quantum Processing

The best and most efficient way to transport information is to encode it in light and send it down an optical fiber where it can propagate with low loss and at high data rates. This process is used for information traveling over the Internet. However to manipulate—or process—the information, it is much better to have it in matter form, as you can grab matter and easily change it. In current fiber optical networks, optical pulses are changed to electronic signals at nodes in the network. However, in these systems with existing conversion methods, the full information capacity of light pulses cannot be utilized and maintained. Using instead the methods described above, all information encoded in light—including its quantum character—can be preserved during conversion between light and matter, and the information can be powerfully processed. This is particularly important for creating quantum mechanical analogues of the Internet. Transport and processing of data encoded in quantum states can be used for teleportation and secure encryption. The ability to process quantum information is needed for the development of quantum computers.

Figure 20: Classical computers use bits that can be valued either 0 or 1.

One possible application of the powerful methods for light manipulation described above is in quantum computing. In our current generation of computers, data are stored in memory as bit patterns of 0s and 1s (binary numbers). In a quantum computer, the 1s and 0s are replaced with quantum superpositions of 1s and 0s, called qubits, which can be 0 and 1 at the same time. Such computers, if they can be built, can solve a certain set of hard problems that it would take an ordinary computer a very long time (longer than the life of the universe) to crack. The trick is that because of quantum superposition, the input bit register in a quantum computer can hold all possible input values simultaneously, and the computer can carry out a large number of calculations in parallel, storing the results in a single output register. Here we get to another important aspect of quantum computing: entanglement.

Let's look at a simple case of entanglement, involving a light pulse containing a single photon (i.e., we have a single energy quantum in the light pulse. There is some discussion as to whether this is a case of true entanglement, but it serves to illustrate the phenomenon in any case). If we send the photon onto a beamsplitter, it has to make a choice between two paths. Or rather, quantum mechanics allows the photon to not actually make up its mind: The photon takes both paths at the same time. We can see this through interference patterns that are made even when the photon rate is so low that less than one photon is traveling at a time. But if we set up a light detector to monitor one of the two paths, we will register a click (a photon hit) or no click, each with a 50% chance. Now say some other (possibly distant) observer sets up a detector to monitor the other path. In this case, if this second observer detects a click, that instantaneously affects our own measurement: We will detect "no click" with 100% probability (or vice versa, an absolutely certain click if the remote observer has detected no click), since each photon can be detected only once. And this happens even in cases where the detectors are at a very large distance from each other. This is entanglement: the quantum correlation of two spatially separated quantum states. The fact that a measurement in one location on part of an entangled state immediately affects the other part of the state in a different location—even if the two locations are separated by a very large distance—is a nonlocal aspect of quantum mechanics. Entangled states are hard to maintain, because interactions with the environment destroy the entanglement. They thus rarely appear in our macroscopic world, but that doesn’t stop them from being essential in the quantum world.

Now that we know what entanglement is, let's get back to the quantum computer. Let's say the quantum computer is set up to perform a particular calculation. One example would be to have the result presented at the output vary periodically with the input value (for example, if the computer calculates the value of the sine function). We wish to find the repetition period. The input and output registers of the computer each consist of a number of quantum bits, and the quantum computation leaves these registers in a superposition of matched pairs, where each pair has the output register holding the function value for the corresponding input register value. This is, in fact, an entangled state of the two registers, and the entanglement allows us to take advantage of the parallelism of the quantum computation. As in the beamsplitter example described above, a measurement on the output register will immediately affect the input register that will be left holding the value that corresponds to the measured output value. If the output repeats periodically as we vary the input, many inputs will correspond to a particular output, and the input register ends up in a superposition of precisely these inputs. This represents a great advantage over a classical calculation: After just one run-through of the calculation, global information—the repetition period—is contained in the input register. After a little "fiddling," this period can be found and read back out with many fewer operations than a classical computer requires. In a classical calculation, we would have to run the computation many times—one for each input value—to slowly, step by step, build up information about the periodicity.

Figure 22: A two-bit quantum computer implemented with two beryllium ions trapped in a slit in an alumina substrate with gold electrodes.

Whether quantum computers can be turned into practical devices remains to be seen. Some of the questions are: Can the technology be scaled? That is, can we generate systems with enough quantum bits to be interesting? Is the processing (the controlled change of quantum states) fast enough that it happens before coupling to the surroundings leads to "dephasing," that is to destruction of the superposition states and the entanglement? Many important experiments aimed at the implementation of a quantum computer have been performed, and quantum computing with a few qubits has been successfully carried out, for example, with ions trapped in magnetic traps (See Figure 22). Here, each ion represents a quantum bit, and two internal states of the ion hold the superposition state corresponding to the quantum value of the bit. Encoding quantum bits—or more generally quantum states—via slow light-generated imprints in Bose-Einstein condensates presents a new and interesting avenue toward implementation of quantum computation schemes: The interactions between atoms can be strong, and processing can happen fast. At the same time, quantum dephasing mechanisms can be minimized (as seen in the experiments with storage times of seconds). Many light pulses can be sent into a Bose-Einstein condensate and the generated matter copies can be stored, individually manipulated, and led to interact. One matter copy thus gets affected by the presence of another, and these kinds of operations—called conditional operations—are of major importance as building blocks for quantum computers where generation of entanglement is essential. After a series of operations, the resulting quantum states can be read back out to the optical field and communicated over long distances in optical fibers.

The transfer of quantum information and correlations back and forth between light and matter in Bose-Einstein condensates may allow for whole new processing algorithms where the classical idea of bit-by-bit operations is replaced by global processing algorithms where operations are performed simultaneously on 3D input patterns, initially read into a condensate, and with use of the full coherence—phase-lock nature—of the condensate. Fundamental questions, regarding the information content of condensates, for example, will need to be addressed.

Figure 23: A Bose-Einstein condensate as a novel processor for quantum information.

Another potential application of slow light-based schemes for quantum information processing, which has the promise to be of more immediate, practical use, is for secure encryption of data sent over a communication network (for example, for protecting your personal information when you send it over the Internet). Entangled quantum states can be used to generate secure encryption keys. As described above with the photon example, two distant observers can each make measurements on an entangled state. If we make a measurement we will immediately know what the other observer will measure. By generating and sharing several such entangled quantum states, a secure encryption key can be created. The special thing with quantum states is that if a spy listens in during transmission of the key, we would know: If a measurement is performed on a quantum state, it changes—once again: The wavefunction "collapses." So the two parties can use some of the shared quantum states as tests: They can communicate the result of their measurements using their cell phones. If there is not a complete agreement between expected and actual measurements at the two ends, it is a clear indication that somebody is listening in and the encryption key should not be used.

An efficient way to generate and transport entangled states can be achieved with the use of light (as in our photon example above) transmitted in optical fibers. However, the loss in fibers is not negligible, and entanglement distribution over long distances (above 100 km, say) has to be made in segments. Once the individual segments are entangled, they must then be connected in pairs to distribute the entanglement between more distant locations. For this to be possible, we must be able to sustain the entanglement achieved in individual segments such that all the segments can eventually be connected. And here, the achievement of hold times for light of several seconds, as described above, is really important.

Figure 24: Was Newton right after all: "Are not gross Bodies and Light convertible into one another... ?"

There are numerous applications for slow and stopped light, and we have explored just a few of them here. The important message is that we have achieved a complete symmetry between light and matter, and we get there by making use of both lasers and Bose-Einstein condensates. A light pulse is converted to matter form, and the created matter copy—a perfect imitation of the light pulse that is extinguished—can be manipulated: put on the shelf, moved, squeezed, and brought to interact with other matter. At the end of the process, we turn the matter copy back into light and beam it off at 186,000 miles per hour. During formation of the matter copy—by the slowing and imprinting of the input light pulse in a Bose-Einstein condensate—it is essential that the coupling laser field is present with its many photons that are all in lock-step. And when the manipulated matter copy is transformed back into light, the presence of many atoms in the receiver (or host) BEC that are all in lock-step is of the essence.

So, we have now come full circle: From Newton over Huygens, Young, and Maxwell, we are now back to Newton:

In Opticks, published in 1704, Newton theorized that light was made of subtle corpuscles and ordinary matter of grosser corpuscles. He speculated that through an alchemical transmutation, "Are not gross Bodies and Light convertible into one another, ...and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?"